Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Gain of Regularity in Extension Problem on Convex Domains Tue, 21 Jul 2015 08:18:10 +0000 We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constant such that on Bergman spaces with there appears the so-called “gain regularity.” The constant depends on the minimum of the dimension and the codimension of the subvariety. This means that the space of functions which admit an extension to a function in the Bergman space is strictly larger than , where is a subvariety. M. Jasiczak Copyright © 2015 M. Jasiczak. All rights reserved. The Spaces of Functions of Two Variables of Bounded -Variation in the Sense of Schramm-Korenblum Tue, 07 Jul 2015 06:53:59 +0000 The purpose of this paper is twofold. Firstly, we introduce the concept of bounded -variation in the sense of Schramm-Korenblum for real functions with domain in a rectangle of . Secondly, we study some properties of these functions and we prove that the space generated by these functions has a structure of Banach algebra. A. Azócar, O. Mejía, N. Merentes, and S. Rivas Copyright © 2015 A. Azócar et al. All rights reserved. On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces Thu, 02 Jul 2015 11:58:57 +0000 In the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm. Nawab Hussain, Giuseppe Marino, and Badriah A. S. Alamri Copyright © 2015 Nawab Hussain et al. All rights reserved. Multiplicative Isometries on Classes of Holomorphic Functions Mon, 29 Jun 2015 08:32:25 +0000 In (Iida and Kasuga 2013), the authors described multiplicative (but not necessarily linear) isometries of onto in the case of positive integer , where    is included in the Smirnov class . In this paper, we will generalize the result to arbitrary (not necessarily positive integer) value of the exponents . Yasuo Iida and Kazuhiro Kasuga Copyright © 2015 Yasuo Iida and Kazuhiro Kasuga. All rights reserved. A Simple Repairable System with Warning Device Thu, 25 Jun 2015 11:14:21 +0000 This paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described into a group of integrodifferential equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory or semigroup theory and the spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes and profit of systems with and without warning device) as well as numerical examples are presented at the end of the paper. Xiao Zhang and Lina Guo Copyright © 2015 Xiao Zhang and Lina Guo. All rights reserved. Commutators of Multilinear Singular Integrals on Weighted Herz Spaces Tue, 23 Jun 2015 10:38:04 +0000 Suppose , is the iterated commutator of and the -linear Calderón-Zygmund operator . The purpose of this paper is to discuss the boundedness properties of on weighted Herz spaces with general Muckenhoupt weights. Baozhen Wang and Huimin Wang Copyright © 2015 Baozhen Wang and Huimin Wang. All rights reserved. Generalized Projections on Closed Nonconvex Sets in Uniformly Convex and Uniformly Smooth Banach Spaces Tue, 23 Jun 2015 06:56:31 +0000 The present paper is devoted to the study of the generalized projection , where is a uniformly convex and uniformly smooth Banach space and is a nonempty closed (not necessarily convex) set in . Our main result is the density of the points having unique generalized projection over nonempty close sets in . Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented. Messaoud Bounkhel Copyright © 2015 Messaoud Bounkhel. All rights reserved. Existence Results for New Weak and Strong Mixed Vector Equilibrium Problems on Noncompact Domain Mon, 22 Jun 2015 11:18:01 +0000 We introduce and consider two new mixed vector equilibrium problems, that is, a new weak mixed vector equilibrium problem and a new strong mixed vector equilibrium problem which are combinations of certain vector equilibrium problems, and vector variational inequality problems. We prove existence results for the problems in noncompact setting. Ali Farajzadeh, Kasamsuk Ungchittrakool, and Apisit Jarernsuk Copyright © 2015 Ali Farajzadeh et al. All rights reserved. The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces Mon, 22 Jun 2015 10:05:32 +0000 This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type: , , . Under some conditions, we prove that this equation is locally well-posed in Besov space . Furthermore, we study the continuity of the solution map for this equation in . Our work improves some earlier results. Yun Wu, Zhengrong Liu, and Xiang Zhang Copyright © 2015 Yun Wu et al. All rights reserved. Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space Mon, 22 Jun 2015 07:01:44 +0000 This paper is concerned with the following nonlinear second-order nonautonomous problem: , where , , and , are not periodic in and is a continuous function and with . The existence and multiplicity of fast homoclinic solutions are established by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory. Qiongfen Zhang and Yuan Li Copyright © 2015 Qiongfen Zhang and Yuan Li. All rights reserved. Long Time Decay Rate to a Bipolar Quantum Drift-Diffusion Model Thu, 18 Jun 2015 08:14:03 +0000 This paper is devoted to studying the long time behavior of solutions to a bipolar quantum hydrodynamic in one-dimensional space for general pressure functions. The model is usually applied to simulate some quantum effects in semiconductor devices. The decay rate for time variable is obtained by the entropy functional method and semidiscrete technique. Yingjie Zhu, Bo Liang, and Xiting Peng Copyright © 2015 Yingjie Zhu et al. All rights reserved. Invertible Weighted Composition Operators on the Fock Space of Wed, 17 Jun 2015 08:08:55 +0000 We give a complete characterization of bounded invertible weighted composition operators on the Fock space of . Liankuo Zhao Copyright © 2015 Liankuo Zhao. All rights reserved. Weighted BMO Estimates for Toeplitz Operators on Weighted Lebesgue Spaces Tue, 16 Jun 2015 10:28:55 +0000 The authors establish the weighted BMO estimates for a class of Toeplitz operators related to strongly singular Calderón-Zygmund operators on weighted Lebesgue spaces. Moreover, the corresponding result for the Toeplitz operators related to classical Calderón-Zygmund operators can be deduced. Yan Lin and Mengmeng Zhang Copyright © 2015 Yan Lin and Mengmeng Zhang. All rights reserved. On the Geometry of Müntz Spaces Tue, 16 Jun 2015 08:55:42 +0000 Let satisfy , and . We investigate the Müntz spaces for . We show that, for each , there is a Müntz space which contains isomorphic copies of all Müntz spaces as complemented subspaces. is uniquely determined up to isomorphisms by this maximality property. We discuss explicit descriptions of . In particular is isomorphic to a Müntz space where consists of positive integers. Finally we show that the Banach spaces for and for are always isomorphic to suitable Müntz spaces if the are the spans of arbitrary finitely many monomials over . Sergey V. Ludkovsky and Wolfgang Lusky Copyright © 2015 Sergey V. Ludkovsky and Wolfgang Lusky. All rights reserved. Note on Order-Isomorphic Isometric Embeddings of Some Recent Function Spaces Mon, 08 Jun 2015 07:59:54 +0000 We investigate certain recently introduced ODE-determined varying exponent spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent space. Moreover, this can be accomplished in a natural unified fashion. This leads to order-isomorphic isometric embeddings of all of the above spaces to an ultrapower of the above varying exponent space. Jarno Talponen Copyright © 2015 Jarno Talponen. All rights reserved. Space of Functions with Some Generalization of Bounded Variation in the Sense of de La Vallée Poussin Thu, 04 Jun 2015 10:25:00 +0000 We introduce a function space with some generalization of bounded variation in the sense of de la Vallée Poussin and study some of its properties, like embeddings and decompositions, among others. René Erlín Castillo, Humberto Rafeiro, and Eduard Trousselot Copyright © 2015 René Erlín Castillo et al. All rights reserved. Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces Wed, 03 Jun 2015 11:18:26 +0000 We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic. Zoryana Mozhyrovska and Andriy V. Zagorodnyuk Copyright © 2015 Zoryana Mozhyrovska and Andriy V. Zagorodnyuk. All rights reserved. On Interval-Valued Pseudolinear Functions and Interval-Valued Pseudolinear Optimization Problems Tue, 02 Jun 2015 10:55:03 +0000 Some basic characterizations of an interval-valued pseudolinear function are derived. By means of the properties of interval-valued pseudolinearity, a class of interval-valued pseudolinear programs is considered, and the solution set of the interval-valued pseudolinear optimization problem is characterized. Jianke Zhang, Qinghua Zheng, Chang Zhou, Xiaojue Ma, and Lifeng Li Copyright © 2015 Jianke Zhang et al. All rights reserved. Local Good- Estimate for the Sharp Maximal Function and Weighted Morrey Space Mon, 01 Jun 2015 13:54:22 +0000 We give a characterization of weighted Morrey space by using Fefferman and Stein’s sharp maximal function. For this purpose, we consider a local good- inequality. Yasuo Komori-Furuya Copyright © 2015 Yasuo Komori-Furuya. All rights reserved. Some Topological and Geometric Properties of Some New Spaces of -Convergent and Bounded Series Mon, 01 Jun 2015 11:09:56 +0000 The main purpose of this study is to introduce the spaces , , and which are -spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spaces , , and , respectively, and derive some inclusion relations. Additionally, Schauder bases of the spaces and have been constructed and the -, -, and -duals of these spaces have been computed. Besides, we characterize some matrix classes from the spaces , , and to the spaces , , and , where . Finally, we examine some geometric properties of these spaces as Gurarǐ’s modulus of convexity, property , property , property WORTH, nonstrict Opial property, and weak fixed point property. Meltem Kaya and Hasan Furkan Copyright © 2015 Meltem Kaya and Hasan Furkan. All rights reserved. A Continuous Characterization of Triebel-Lizorkin Spaces Associated with Hermite Expansions Thu, 28 May 2015 14:32:36 +0000 We study the properties of the Triebel-Lizorkin spaces associated with the multidimensional Hermite expansions on (). In addition to the endpoint estimates, we give the continuous characterizations of these spaces via harmonic and thermic extensions from into . Based on this result, we obtain the boundedness of Riesz transform associated with the Hermite expansions. Shuli Gong, Bolin Ma, and Zunwei Fu Copyright © 2015 Shuli Gong et al. All rights reserved. Fredholm Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions of Type Wed, 27 May 2015 09:05:14 +0000 We study Fredholm (weighted) composition operators between general weighted Banach spaces of analytic functions on the open unit disc with sup-norms. M. Carmen Gómez-Collado and David Jornet Copyright © 2015 M. Carmen Gómez-Collado and David Jornet. All rights reserved. On Pointwise Approximation of Conjugate Functions by Some Hump Matrix Means of Conjugate Fourier Series Tue, 26 May 2015 05:50:41 +0000 The results generalizing some theorems on summability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated. W. Łenski and B. Szal Copyright © 2015 W. Łenski and B. Szal. All rights reserved. A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents Thu, 21 May 2015 12:51:46 +0000 It is proven that if in a bounded domain and if for some , then given , the Hardy-Littlewood maximal function of , , is such that . Because , the thesis is slightly weaker than for some . The assumption that for some is proven to be optimal in the framework of the Orlicz spaces to obtain in the same class of spaces. Alberto Fiorenza Copyright © 2015 Alberto Fiorenza. All rights reserved. Fixed Point Theorems with Applications to the Solvability of Operator Equations and Inclusions on Function Spaces Wed, 20 May 2015 13:36:23 +0000 Nawab Hussain, Jesus Garcia-Falset, Mohamed-Aziz Taoudi, and Calogero Vetro Copyright © 2015 Nawab Hussain et al. All rights reserved. Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems Wed, 20 May 2015 08:26:57 +0000 Hemant Kumar Nashine, Mujahid Abbas, Marlène Frigon, and Calogero Vetro Copyright © 2015 Hemant Kumar Nashine et al. All rights reserved. Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities Tue, 19 May 2015 11:32:44 +0000 We introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepest-descent method, and Mann’s iteration method. We prove that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions, and the solution set of general system of variational inequalities (GSVI), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm for solving a hierarchical variational inequality problem with constraints of finitely many GMEPs, finitely many variational inclusions, and the GSVI. The results obtained in this paper improve and extend the corresponding results announced by many others. L. C. Ceng, A. Latif, C. F. Wen, and A. E. Al-Mazrooei Copyright © 2015 L. C. Ceng et al. All rights reserved. A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition Tue, 19 May 2015 11:31:16 +0000 We establish a new Lyapunov-type inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain Mittag-Leffler functions has no real zeros. Mohamed Jleli, Lakhdar Ragoub, and Bessem Samet Copyright © 2015 Mohamed Jleli et al. All rights reserved. Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function Tue, 19 May 2015 08:28:44 +0000 We are concerned with the following third-order boundary value problem with integral boundary condition:      where , and . Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained. Bing-Wei Niu, Jian-Ping Sun, and Qiu-Yan Ren Copyright © 2015 Bing-Wei Niu et al. All rights reserved. Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces Tue, 19 May 2015 07:31:25 +0000 This paper investigates properties of convergence of distances of -cyclic contractions on the union of the subsets of an abstract set defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of -cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the -composite mappings restricted to each of the subsets in the cyclic disposal are also investigated and some illustrative examples are given. Manuel De la Sen and Erdal Karapınar Copyright © 2015 Manuel De la Sen and Erdal Karapınar. 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